#14630: Add `simplify_real` method to symbolic expressions
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Reporter: mjo | Owner: burcin
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.10
Component: symbolics | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Michael Orlitzky | Merged in:
Dependencies: | Stopgaps:
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Comment (by mjo):
Replying to [comment:2 kcrisman]:
> You need to do `\left|x\\right|`.
>
[[BR]]
Fixed in the new patch, but my MathJAX still doesn't work, so please give
it a look.
[[BR]]
>
> I'm not sure about all the stuff in the doc and the code, but I think
that some of the doc is doing the code and vice versa? For instance,
> {{{
> # Forget all assumptions
> }}}
> but you don't do that in the code.
[[BR]]
Whoops, I forgot to call `forget()`; the comment was correct. I fixed it
and added a doctest to ensure that no new assumptions remain after the
call.
[[BR]]
> And the corresponding part in the doc seems to imply that in order to
use `simplify_real` you have to assume variables are real... I may be
misunderstanding something here. I think this could be a good way to
solve the issue at hand.
[[BR]]
I didn't mean that the user has to `assume()` anything, only that we have
to assume things are real in the traditional sense. You can call
`simplify_real()` on an expression containing complex variables, but the
answer might not make sense.
[[BR]]
>
> My question is how this will interact with the other simplifications. I
seem to recall that in some of the more controversial (e.g.
`radcan`-related) simplifications we do, part of the issue is whether the
variable is real... that recollection may be outdated. Anyway, I could
imagine that `simplify_foo` simplified differently whether one was real or
complex, though I hesitate to add `simplify_foo_real` for all `foo`!
[[BR]]
Expressions ''should'' be complex everywhere. I believe there are one or
two functions which treat them as real, but they're documented to do that,
so it's fine. Radcan via `simplify_radical()` will still produce crazy
answers that are invalid for complex numbers, but there isn't much that
can be done about that now except revoke the name "simplify" from
"simplify_radical."
Not many expressions are actually affected by the domain and 'real'
assumptions. We can get most of the benefit of `simplify_foo_real()` by
doing `simplify_foo().simplify_real()`. Simplifications can be
combined/repeated to produce better answers, and we already have a
situation where calling e.g. `simplify_full()` twice might give you a
better answer than calling it once. So you're kind of on your own
regarding how many simplifications to try and in what order.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14630#comment:3>
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